CURITIBA, Brazil—Investigations into Brazil’s embattled construction giant Odebrecht SA are exposing a larger network of graft in Latin America than was already revealed in a massive anticorruption settlement, according to prosecutors in several countries.

Since the firm admitted in December to paying nearly $800 million in bribes, authorities across Latin America have launched new investigations that are beginning to ensnare former high-ranking officials and other companies beyond Odebrecht.

In Peru, a judge issued an arrest warrant for a former president suspected of taking a kickback. In Argentina, a prosecutor opened a probe into alleged payments to the country’s intelligence chief, while Colombian authorities seized expensive property of a former senator. In Brazil, former President Luiz Inácio Lula da Silva has been charged with arranging loans from the country’s development bank, BNDES, to help Odebrecht win projects abroad in exchange for personal benefits. All have denied wrongdoing.

Brazilian prosecutors, who worked closely with Swiss and U.S. officials in reaching the initial settlement to resolve criminal charges, say they believe the number of people investigated could more than double. In the December deal, the largest ever of its kind, Odebrecht agreed to pay between $2.6 billion to $4.5 billion in fines. Separate claims from other countries could add to that, the Brazilian prosecutors say. Odebrecht says it is cooperating with prosecutors in other Latin American countries “to clarify acts practiced by the company.”

“This [investigation] has the potential to spread, no doubt,” said Orlando Martello Junior, a Brazilian prosecutor.

Colombia’s Attorney General Nestor Martínez said recently his investigators found a web of bribery in the country extending beyond the $11 million in corrupt payments Odebrecht acknowledged in the settlement. On Thursday, an official at state-run Banco Agrario was indicted on a charge of allegedly falsifying documents that helped an Odebrecht-controlled consortium secure generous loan terms for a river-expansion project. The bank didn’t respond to a request for comment, and the official isn’t expected to enter a plea until his first hearing on March 15.

In Peru, Attorney General Pablo Sánchez said prosecutors have launched over 30 investigations involving Odebrecht and other Brazilian construction firms. Graña y Montero, Peru’s biggest builder and a frequent Odebrecht partner, could also be investigated, an official said Thursday. That followed press reports citing claims from the former head of Odebrecht in Peru that Graña y Montero knew bribes were paid in connection to a joint project.

The allegations, coupled with a sharp decline in the company’s share price, led to the resignations last week of its chairman, chief executive and a director. Last week, a class-action lawsuit was filed in a New York court alleging that Graña y Montero violated the Securities Exchange Act by making false or misleading statements and failing to disclose it was aware of Odebrecht’s bribes. Graña y Montero denies it had knowledge of the illegal payments.

As new details emerge from countries across the region, investors are selling off Odebrecht debt on fears the company will face further legal action or be barred from doing business outside Brazil. The firm’s 2025 bonds are trading at 39.9 cents on the dollar, down nearly 30% so far this year, according to FactSet.

“There are a lot of ongoing investigations in other countries and [they] are likely to reach and damage the company even more,” said Paulo Petrassi, a partner in Brazilian investment firm Leme Investimentos.

In January, the attorney general’s office of Peru said prosecutors signed a deal with Odebrecht to provide information on bribes, an action whose consequences continue to ricochet through the country’s establishment.

Former President Alejandro Toledo, who governed from 2001 to 2006, denied charges that he took $20 million in bribes that prosecutors say were wired to offshore accounts of businesses owned by a close friend.

Last month, a court ordered the arrest of Mr. Toledo, whom prosecutors are trying to extradite from the U.S., after prosecutors laid out allegations that he secretly met with an Odebrecht executive in 2004 in the presidential suite of the Hotel Marriott in Rio de Janeiro. There, prosecutors say, the then-president and three associates allegedly worked out a bribe in exchange for giving Odebrecht lucrative contracts to build two stretches of a highway project.He has denied the charge. Peru’s comptroller general says the cost of the entire project ballooned to about $4 billion from original bids totaling $1 billion.

Another ex-president, Ollanta Humala, who governed until last year, has denied accusations from a former Odebrecht director that his wife took $3 million in cash from the firm for his campaign. His wife, Nadine Heredia, has said she didn’t receive the money.

On Monday, Katherine Ampuero, an attorney appointed to represent the state of Peru in the Odebrecht case, asked the attorney general’s office to open an investigation into yet another former president, Alan García, who was in power from 2006 to 2011, over corruption allegations tied to Lima’s subway project. Mr. García has denied taking bribes.

Ms. Ampuero also asked prosecutors to open a preliminary investigation into sitting President over claims that Odebrecht made payments to a company with ties to him. Mr. Kuczynski has in the past denied wrongdoing.Pedro Pablo Kuczynski

Mr. Kuczynski, who was Mr. Toledo’s finance minister, said his government would triple the budget allocated to anticorruption prosecutors, create a system to protect and compensate whistleblowers, and prohibit corrupt companies from transferring funds abroad before paying fines.

“We need a radical change,” said Mr. Kuczynski, whose approval rating has fallen in recent months to a low of 29% on concerns about corruption. “This crisis of confidence began in Brazil and has now extended to all of Latin America’s countries.”

In Mexico, Odebrecht has admitted paying $10.5 million in bribes. Investigators there say they are looking not only at some $1.6 billion in contracts Odebrecht won from state-run oil giant Petróleos Mexicanos, but also at 11 additional contracts Pemex awarded to Odebrecht subsidiaries under different names. The total amount of contracts under review comes to more than $2 billion, according to people familiar with the investigation.

Write to Ryan Dube at ryan.dube@dowjones.com, Luciana Magalhaes at Luciana.Magalhaes@wsj.com and Rogerio Jelmayer at rogerio.jelmayer@wsj.com

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